MTB cassette with a 36T sprocket should drop straight on. The 105 rear mech may cope, but if not get the best 9 speed MTB rear mech you can. 10 speed mtb mechs won't index with STIs.
This is what I've done, on a number of bikes.
For example, my custom ti touring bike is a wide range triple (with 24t difference which is more than recommended) with 105 front mech, and at the back a 10-speed cassette 11-36 with Shimano Deore rear mech. The front requires a bit of "double declutching" but it all works a treat, with a high gear of 52x11 and a low of 28x36. STI indexing not a problem at all.
As to costs, Shimano MTB cassettes are <£20 and Deore mechs can be got for <£30. No idea on labour costs as this was the spec and parts list I gave Enigma when they built up the bike.
I have also done what
@mmmmartin suggests - I added a 26t granny ring to the 48/36 double that came standard with my Surly Cross Check. Tiagra front mech works just fine -- but did need a new, longer bottom bracket. I was replacing the cranks at the same time. Brixton Cycles did the work. I don't remember what they charged for labour, but I remember being fairly skint at the time and having just coughed up money for a professional bike fit, so it must have been fairly cheap.
ETA: re the Deore mech on the Enigma. This is a 9 speed mech, which works equally well with both 9- and 10-speed cassettes. In fact, it works much better with my 11-36 10-speed cassette than the 10-speed Shimano XT rear mech that Enigma fitted first (as they'd had difficulty sourcing the Deore on my spec list). Fortunately I had several Deore rear mechs in my own stores and was able to swap it out as the XT was actually pretty useless.